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Question 222910: Dear Sir:
I am trying to solve the following equation for x:
y = {e^x} / {1 + 2e^x}
I have tried various approaches but they do not seem to work:
(1) multiplying both sides of the equation by the value of the denominator and then taking the logarithms of both sides.
(2) rewriting the equation using fractional exponents and then trying to simplify the right hand side before taking the logarithm of both sides
But, of course when I take the logarithm of both sides I cannot separate the expression in the parenthesis. Obviously, I am on the wrong track, but I have not found any help in my math books or my professor's notes.
Is it possible for you to help me. I would be very grateful for advise and an illustration of the appropriate method.
Very truly yours,
Lawrence G. Lever (an older student returning to mathematics after many years)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! y = {e^x} / {1 + 2e^x}
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Cross multiply to get:
y + 2ye^x = e^x
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Get the e^x terms together:
2ye^x-e^x = -y
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Factor out the e^x:
e^x(2y-1) = -y
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Divide thru by 2y-1 to get
e^x = -y/(2y-1)
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Take the natural log to solve for x
x = ln[-y/(2y-1)]
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Cheers,
Stan H.
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